Question: Solve for $x$ and $y$ using elimination. ${-x+5y = 3}$ ${x+6y = 8}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the top and bottom equations together. $11y = 11$ $\dfrac{11y}{{11}} = \dfrac{11}{{11}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {-x+5y = 3}\thinspace$ to find $x$ ${-x + 5}{(1)}{= 3}$ $-x+5 = 3$ $-x+5{-5} = 3{-5}$ $-x = -2$ $\dfrac{-x}{{-1}} = \dfrac{-2}{{-1}}$ ${x = 2}$ You can also plug ${y = 1}$ into $\thinspace {x+6y = 8}\thinspace$ and get the same answer for $x$ : ${x + 6}{(1)}{= 8}$ ${x = 2}$